Chapter 4. Superconducting and Quantum-Effect Devices
Chapter 4. Superconducting and Quantum-Effect Devices
Academic and Research Staff
Professor Terry P. Orlando, Dr. Chagarn B. Whan
Visiting Scientists and Research Affiliates
Dr. Herre S.J. van der Zant
Graduate Students
Martin Burkhardt, David J. Carter, Janet A. Cutro, Amy E. Duwel, Arvind Kumar, Mark R. Schweizer, Ilia
Sokolinski, Enrique Trias
Undergraduate Students
Vjekoslav Svilan
Technical and Support Staff
Charmaine A. Cudjoe-Flanders, Angela R. Odoardi
4.1 Nonlinear Dynamics of Discrete
Josephson Arrays
agation makes discrete Josephson rings ideal
systems for further quantum vortex experiments.
Sponsor
4.2 Resonance Splitting in Inductively
Coupled Arrays
National Science Foundation
Grant DMR 94-02020
Project Staff
Dr. Herre S.J. van der Zant, Professor Terry P.
Orlando, S. Watanabe, S. Strogatz
We have studied the dynamics of circular onedimensional arrays of underdamped Josephson
junctions connected in parallel. In these Josephson
rings, a single vortex can be trapped and studied
experimentally without complications caused by
reflections off boundaries. We find that a propagating vortex can become phase-locked to linear
waves excited in its wake. In the I-V curve, resonant steps are observed indicative of this phaselocking. Numerical simulations indicate that, at
least in principle, an infinite number of these steps
is possible. Resonant steps also occur in the I-V
curves for higher voltages in the return path of the
subgap region. These resonant steps have a completely different origin and occur at voltages where
the periodic whirling solution undergoes an instability parametrically amplified by the linear modes in
the system. Only N/2 steps are possible with N the
number of junctions in the ring. Despite the presence of linear modes, our numerical studies show
that a single propagating vortex can, for a certain
range of parameters, be viewed as a particle with a
long mean free path. This almost free vortex prop-
Sponsor
National Science Foundation
Fellowship MIP 88-58764
Grant DMR 94-02020
Project Staff
Amy E. Duwel, Enrique Trias, Professor Terry P.
Orlando, Dr. Herre S.J. van der Zant, S. Watanabe,
S. Strogatz
Coupled arrays of one- and two-dimensional
Josephson junctions have received renewed attention as model systems for high-temperature superconducting thin films of BSCCO and TBCCO,
showing coupling of the discrete layers. These
arrays are also of interest since phase locking
between the coupled rows decreases the linewidth
of the radiation emitted by oscillators made of these
arrays.
We have observed that, in long inductively coupled
arrays of niobium Josephson junctions, two Eck
steps appear in the current-voltage (I-V) characteristic. These steps correspond to arrays of vortices
traveling through the system. The wave is composed of nearly a single harmonic with a welldefined amplitude and dispersion relation. We have
found that the lower step corresponds to an anti-
Chapter 4. Superconducting and Quantum-Effect Devices
symmetric state where the voltages are oscillating
out of phase between the two rows. However, the
upper step corresponds to a symmetric state, where
the oscillating voltages are in-phase. We have
found an analytical ansatz for the voltage states
which is close to numerical observations. We can
analytically predict the DC voltages of these resonant states and numerically predict the amplitude of
the AC voltages.
The upper step can have important technological
implications. When the system is biased in this
state, the AC voltages add, increasing the power
output. The two-row device will also have higher
output impedance than its continuous, stacked junction counterpart. These qualities make this device
desirable for oscillator applications. As in a single
row of a discrete array, the frequencies can be
tuned with a control current and are stable for a relatively wide range of bias currents. Although the
bandwidth is approximately the same as for the
single row, a larger output resistance may increase
the linewidth. However, phase locking between the
two rows is expected to reduce the linewidth, and
such measurements will be helpful.
4.3 Flux Flow and Self Field Effects
Sponsor
National Science Foundation
Fellowship MIP 88-58764
Grant DMR 94-02020
Project Staff
Enrique Trias, Dr. Herre S.J. van der Zant, Professor Terry P. Orlando
Measurements and numerical studies of the selfinduced magnetic field effects on flux flow in twodimensional arrays of niobium Josephson junctions
have been performed. It was found that the fluxflow resistance becomes larger as the penetration
depth of the array decreases. A phenomenological
model, which agrees qualitatively with the experiments and simulations, has been developed to
explain the self-field effects on flux flow. The main
conclusion is that both the mass of the vortex and
the array viscosity decrease due to the smaller
spatial extent of the vortex current caused by the
self-fields.
Vortices in the flux-flow region are localized and,
because of the electrical energy in the junctions,
1 U.S. Air Force, Rome Laboratory, Rome, New York.
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RLE Progress Report Number 138
can be treated as massive particles. The applied
field specifies the density of vortices present in the
array. With this density, the driving force, and the
viscosity, we model the dependence of the flux-flow
resistance in terms of the array parameters, A_ and
Ic and applied magnetic field, f. A linear dependence of the flux-flow resistance Rff versus f is
found.
It has also been shown that Rf, is dependent on
both A. and Pc. The dependence on ic follows
from spin-wave damping while the Al dependence
is a result of a reduction of the viscosity caused by
the decreasing physical size of traveling vortices as
AL decreases.
This simple phenomenological
model gives a qualitative as well as a semiquantitative description of the dynamics.
The
effects can also be seen in numerical simulations
that take into account all the mutual inductances
between cell pairs.
However, the flux-flow region appears to be richer
in its dynamics than the presented model can
account for. For small arrays, there is a spatial
dependence of the flux-flow region which we have
measured and also seen in simulations. Different
rows have different flux-flow slopes and the outer
rows closest to the edge appear to have almost no
flux-flow associated with them. Though these deviations do not diminish the useful and intuitive
results from the phenomenological model, they do
point to further research on flux flow.
4.4 Triangular Arrays of Josephson
Junctions
Sponsors
U.S. Air Force - Office of Scientific Research
Grant F30602-96-1-0059
Rome Laboratory
Project Staff
Amy E. Duwel, Professor Terry P. Orlando, S.
Yukon1
Superconducting arrays of Josephson junctions are
important devices for coherent sources of lowpower radiation in millimeter and sub-millimeter
regime.
One- and two-dimensional arrays of
Josephson junctions are of particular importance
because the phase-locking among the junctions
overcomes many of the problems of low
impedances and power levels of a single junction.
Chapter 4. Superconducting and Quantum-Effect Devices
Coherent microwave radiation has been observed
in square arrays of Josephson junctions.
In novel geometries based on triangular rather than
square arrays, numerical simulations and calculations show a novel and technologically important
dynamical state. This state has junctions which
generate microwave current and radiation without
"going over the top" and producing a DC power
loss.
We are developing techniques for designing triangular arrays of Josephson junctions within standard
superconducting foundry capabilities. These arrays
are predicted to generate AC current without a DC
component, and we will explore the feasibility of
making microwave measurements on these and
other types of Josephson arrays.
4.5 One-dimensional Parallel
Josephson-junction Arrays as a Tool
For Diagnostics
Sponsor
Defense Advanced Research Projects Agency/
Consortium for Superconducting Electronics
Contract MDA 972-90-C-0021
Project Staff
Dr. Herre S.J. van der Zant, Professor Terry P.
2
Orlando, in collaboration with A. W. Kleinsasser
We propose and demonstrate the use of underparallel arrays of
one-dimensional
damped,
Josephson junctions as a tool for circuit diagnostics.
By measuring the Fiske modes and the critical
current in a magnetic field, we determined the self
and nearest-neighbor inductances as well as the
capacitances of single junctions. We have used
this technique to find the capacitance of
Nb-Al 20-Nb junctions for critical current densities
of 0.3 - 20 kA/cm2. We find that the specific capacitance increases by about a factor of two over this
range. This increase has important consequences
for the design of single-flux-quantum circuits and
SQUIDs. Measurement of the junction capacitance
for critical current densities of 100 kA/cm2 is possible, but requires submicrometer junctions with
dimensions of the order of 0.3 pm.
4.6 Quantum Device Simulations
Sponsor
National Science Foundation
Grant DMR 94-02020
Project Staff
Dr. Chagarn B. Whan, Professor Jacob K. White,
Professor Terry P. Orlando
We numerically calculated the full capacitance
matrices for both one-dimensional (1-D) and twodimensional (2-D) quantum-dot arrays. We find that
it is necessary to use the full capacitance matrix in
modeling coupled quantum dots due to weaker
screening in these systems in comparison with
arrays of normal metal tunnel junctions. The static
soliton (a fundamental electronic charge in the
entire array) potential distributions in both 1-D and
2-D arrays are well approximated by the
unscreened (l/r) coulomb potential, instead of the
exponential fall-off expected from the often used
nearest- neighbor approximation. In terms of dynamics, we compare the current-voltage (I-V) characteristics of voltage biased 1-D arrays using either
the full capacitance matrix or its nearest-neighbor
approximation. The I-V curves show clear differences and the differences become more pronounced when larger arrays are considered.
For quantum dot arrays made by electrostatic confinement of two-dimensional electron gas (2DEG) in
GaAs/AIGaAs heterostructures, the array forms a
co-planar structure with all dots residing in the
2DEG plane. The co-planar capacitors are far less
effective than the parallel plates in terms of confining electric field. Therefore, in comparison with
tunnel junction arrays, the field lines originating
from one of the quantum dots are much less confined and can reach out to dots that are much
further apart. A model that considers only the
nearest-neighbor capacitive coupling is unlikely to
be accurate in this situation. We now give a more
quantitative analysis of this problem.
In our model, the quantum dots (small puddles of a
2DEG) are treated as thin circular shaped conducting plates, with diameter D = 1 pm. The plates
are arranged to form either 1-D or 2-D arrays with
lattice constant a = D + d = 1.1 pm, where d = 0.1
pm is the closest separation between adjacent dots
(or the tunnel barrier width). We believe these
values are reasonable for arrays in the classical
charging regime with weak inter-dot tunneling (i.e.,
2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.
Chapter 4. Superconducting and Quantum-Effect Devices
the tunneling resistance, RT>RoQ h/e 2). Once the
array geometry is specified, we compute the full
capacitance matrix C of the 1-D and 2-D arrays
using FASTCAP, an efficient capacitance extraction
tool.
Field Effects in Arrays of Josephson Junctions."
In Macroscopic Quantum Phenomena and
Coherence in Superconducting Arrays. Eds. C.
Giovannella and M. Tinkham. World Scientific,
1995.
We have calculated the potential distribution due to
a soliton being located at the center of a 21 x 1
series array, using both the full capacitance matrix
and its nearest neighbor approximation.
The
nearest neighbor approximation gives an exponentially decaying soliton potential as expected.
However, the soliton potential distribution that result
from the full capacitance matrix decays much
slower. We find that the soliton potential follows
the simple 1/r law almost exactly over the entire
array, except at the origin where the Coulomb
potential is singular.
Smith, H.I., M.L. Schattenburg, S.D. Hector, J.
Ferrera, E.E. Moon, I.Y. Yang, and M.
Burkhardt. "X-ray Nanolithography: Extension to
the Limits of the Lithographic Process."
Nanotechnology (Special Issue of Microelectronic Engineering). Forthcoming.
We have also computed current-voltage (I-V) characteristics of 1-D quantum dot arrays, which is
experimentally more relevant. The I-V curves are
calculated with both the full capacitance matrix and
the nearest-neighbor approximation. The resulting
I-V curves show many differences. The threshold
voltages are not exactly the same, and the fine
structures are different and become more pronounced when we consider larger arrays. At high
voltage, the two curves merge and become nearly
linear. Hence, we see that the full capacitance
matrix is necessary in the dynamical simulation of
these arrays.
4.7 Publications
Burkhardt, M., H.I. Smith, D.A. Antoniadis, T.P.
Orlando, M.R. Melloch, K.W. Rhee, and M.C.
Peckerar. "Fabrication Using X-ray Nanolithography and Measurement of Coulomb Blockade
in a Variable-Sized Quantum Dot." J. Vac. Sci.
Technol. B 12: 3611-3613 (1994).
Burkhardt, M., D.J.D. Carter, D.A. Antoniadis. T.P.
Orlando, H.I. Smith, M. Melloch, K.W. Rhee, and
M.C. Peckerar.
"Measurement of a Double
Quantum Dot." Submitted to J. Appl. Phys.
Delin, K.A. and T.P. Orlando. "Superconductivity."
In The Engineering Handbook. Ed. R.C. Dorf.
Boca Raton, Florida: CRC Press, 1996.
Duwel, A.E., E. Trias, T.P. Orlando, H.S.J. van der
Zant, S. Watanabe and S. Strogatz. "Resonance
Splitting in Discrete Planar Arrays of Josephson
Junctions." Submitted to J. Appl. Phys..
Orlando, T.P., H.S.J. van der Zant, J. White, E.
Trias, and A. E. Duwel. "Measurements of Self-
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RLE Progress Report Number 138
Trfas, E., T.P. Orlando, and H.S.J. van der Zant.
"Flux Flow in Two-dimensional Arrays of Nb
Josephson Junctions." Submitted to Phys. Rev.
B.
Trfas, E., J.R. Phillips, H.S.J. van der Zant, and
T.P. Orlando. "Self-field Effects in Two Dimensional Nb Josephson-junction Arrays." IEEE
Trans. Appl. Superconduct. 5: 2707 (1995).
van der Zant, H.S.J., T.P. Orlando, and A.W.
Kleinsasser.
"One-dimensional
Parallel
Josephson-junction Arrays as a Tool for Circuit
Diagnostics." IEEE Trans. Appl. Superconduct.
5: 3333-3336 (1995).
van der Zant, H.S.J., T.P. Orlando, S. Watanabe
and S.H. Strogatz.
"Kink Propagation in a
Highly Discrete System: Observation of Phase
Locking to Linear Waves." Phys. Rev. Lett. 74:
174-177 (1995).
van der Zant, H.S.J., T.P. Orlando, S. Watanabe,
and S.H. Strogatz. "Nonlinear Dynamics of Discrete Josephson Rings." In Macroscopic
Quantum Phenomena and Coherence in Superconducting Arrays. Eds. C. Giovannella and M.
Tinkham. World Scientific, 1995.
Watanabe, S., H.S.J. van der Zant, S. Strogatz, and
T.P. Orlando. "Dynamics of Circular Arrays of
Josephson Junctions and the Discrete SineGordon Equation." Submitted to Phys. Rev. D.
Watanabe, S., S. H. Strogatz, H.S.J. van der Zant,
and T. P. Orlando. "Resonant Steps in Parallel
Josephson-junction Arrays: Parametric Instabilities of Whirling Modes." IEEE Trans. Appl.
Superconduct. 5: 2698-2701 (1995).
Watanabe, S., S.H. Strogatz, H.S.J. van der Zant,
and T.P. Orlando. "Whirling Modes and Parametric Instabilities in the Discrete Sine-Gordon
Equation: Experimental Tests in Josephson
Rings." Phys. Rev. Lett. 74: 379-382 (1995).
Chapter 4. Superconducting and Quantum-Effect Devices
Whan, C.B., J. White, and T.P. Orlando. "Full
Capacitance Matrix of Coupled Quantum Dot
Arrays: Static and Dynamical Effects." Submitted to Appl. Phys. Lett.
Theses
Burkhardt, M. Fabrication Technology and Measurement of Coupled Quantum Dot Devices. Ph.D.
diss., Dept. of Electr. Eng. and Comput. Sci.,
MIT, 1995.
Duwel, A.E. Underdamped Vortex Flow Devices.
S.M. thesis, Dept. of Electr. Eng. and Comput.
Sci., MIT, 1995.
Trias, E. Inductance Effects in Two-Dimensional
Arrays of Josephson Junctions. S.M. thesis,
Dept. of Electr. Eng. and Comput. Sci., MIT,
1995.
I q
1 pm
- Ih
At the debutante's ball, young nano-women gather in their finery at the edge of the stage to weep because
the nano-boys won't dance with them.
An array of 50-nm-wide posts with a periodicity of 100 nm. The posts consist of PMMA on top of an antireflection coating (ARC). The substrate consists of a 250-nm-thick layer of silicon nitride on silicon. The
PMMA was exposed using achromatic interferometric lithography. After development of the PMMA, an 02
reactive ion etch was used to etch through the ARC. SEM viewing caused some melting and charging
which resulted in the large gathering of nanopeople. The melting problem was solved by imaging at low
voltage.
Timothy A. Savas, a graduate student in RLE's Quantum-Effects Devices Group, submitted this micrograph,
which won in the most bizarre category at the Electron Ion Photon Beam Technology and Nanofabrication
Conference, Scottsdale, Arizona, in June 1995.
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RLE Progress Report Number 138